Algebra & Number Theory

A $p$-adic Eisenstein measure for vector-weight automorphic forms

Ellen Eischen

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Abstract

We construct a p-adic Eisenstein measure with values in the space of vector-weight p-adic automorphic forms on certain unitary groups. This measure allows us to p-adically interpolate special values of certain vector-weight C∞ automorphic forms, including Eisenstein series, as their weights vary. This completes a key step toward the construction of certain p-adic L-functions.

We also explain how to extend our methods to the case of Siegel modular forms and how to recover Nicholas Katz’s p-adic families of Eisenstein series for Hilbert modular forms.

Article information

Source
Algebra Number Theory, Volume 8, Number 10 (2014), 2433-2469.

Dates
Received: 3 March 2014
Revised: 22 September 2014
Accepted: 3 November 2014
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513730330

Digital Object Identifier
doi:10.2140/ant.2014.8.2433

Mathematical Reviews number (MathSciNet)
MR3298545

Zentralblatt MATH identifier
06387028

Subjects
Primary: 11F03: Modular and automorphic functions
Secondary: 11F33: Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50] 11F30: Fourier coefficients of automorphic forms 11F55: Other groups and their modular and automorphic forms (several variables) 11F85: $p$-adic theory, local fields [See also 14G20, 22E50] 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms

Keywords
Eisenstein measure $p$-adic modular forms $p$-adic automorphic forms Eisenstein series Siegel modular forms automorphic forms on unitary groups

Citation

Eischen, Ellen. A $p$-adic Eisenstein measure for vector-weight automorphic forms. Algebra Number Theory 8 (2014), no. 10, 2433--2469. doi:10.2140/ant.2014.8.2433. https://projecteuclid.org/euclid.ant/1513730330


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